The New Sudoku Players' Forum

by **eleven** » Sun Sep 19, 2021 9:19 pm

Code: Select all: +-------+-------+-------+ | 1 8 . | . . 6 | . . . | | 7 . . | 4 . . | . . . | | . . 3 | . . . | . 6 4 | +-------+-------+-------+ | . 7 8 | 6 . 4 | . . 9 | | . 4 . | 7 . 8 | . 5 . | | . . . | . 5 9 | . . . | +-------+-------+-------+ | . . . | . . . | . 8 . | | . . . | 5 . . | 7 . . | | 4 . 9 | . . . | . . 5 | +-------+-------+-------+

by **shye** » Tue Sep 21, 2021 2:01 am

this puzzle was very hard! im betting theres a trick to it i didnt spot, because the path i got was 4 steps '''>_>

Code: Select all: .--------------.------------------.-------------------. | 1 8 4 | 239 29 6 | 5 2379 237 | | 7 6 5 | 4 #1289 123 | 12389 1239 1238 | | 2 9 3 |#18 7 5 |#18 6 4 | :--------------+------------------+-------------------: | 5 7 8 | 6 *123 4 |*123 123 9 | | 9 4 12 | 7 *123 8 |*1236 5 1236 | | 36 123 126 |#2-1 5 9 | 48 47 78 | :--------------+------------------+-------------------: | 36 5 7 | 1239 12469 123 | 49 8 1236 | | 8 123 126 | 5 49 123 | 7 49 1236 | | 4 123 9 | 1238 #1268 7 |#1236 123 5 | '--------------'------------------'-------------------' 1r45c7 - 1r3c7 ================ 1r3c4 // \\ 1r45c5 \\ => -1r6c4 \\ \\ 6r5c7 - 6r9c7 = (6-8)r9c5 = 8r2c5 - 8r3c4

UR chain
23UR in r45c57, guardians 1r45c57 & 6r5c7
all guardians lead to -1r6c4

few singles and locked candidates

Code: Select all: .-------------.----------------.-------------------. | 1 8 4 | 39 29 6 | 5 2379 237 | | 7 6 5 | 4 #289 123 | 1239-8 1239 #1238 | | 2 9 3 | 18 7 5 | 18 6 4 | :-------------+----------------+-------------------: | 5 7 8 | 6 13 4 | 123 123 9 | | 9 4 2 | 7 13 8 | 136 5 136 | | 36 13 16 | 2 5 9 |#48 47 #78 | :-------------+----------------+-------------------: | 36 5 7 | 139 #46-29 123 |#49 8 1236 | | 8 123 16 | 5 49 123 | 7 49 1236 | | 4 123 9 | 138 #68-2 7 | 1236 123 5 | '-------------'----------------'-------------------'

CNL
(4=8)r6c7 - 8r6c9 = 8r2c9 - 8r2c5 = (8-6)r9c5 = (6-4)r7c5 = 4r7c7 - 4r6c7 loop
=> -8r2c7, -2r9c5, -29r7c5

Code: Select all: .-------------.---------------.------------------. | 1 8 4 |#39 29 6 | 5 2379 237 | | 7 6 5 | 4 289 #13 | 1239 1239 1238 | | 2 9 3 |#18 7 5 | 18 6 4 | :-------------+---------------+------------------: | 5 7 8 | 6 13 4 | 123 123 9 | | 9 4 2 | 7 13 8 | 136 5 136 | | 36 13 16 | 2 5 9 | 48 47 78 | :-------------+---------------+------------------: | 36 5 7 |#39-1 46 123 | 49 8 1236 | | 8 123 16 | 5 49 123 | 7 49 1236 | | 4 123 9 | 138 68 7 | 1236 123 5 | '-------------'---------------'------------------'

l-wing
1r3c4 = (1-3)r2c6 = (3-9)r1c4 = 9r7c4
=> -1r7c4

some pairs, then the hard step:

Code: Select all: .-------------.--------------.------------------. | 1 8 4 |#39 29 6 | 5 2379 #237 | | 7 6 5 | 4 #289 #13 | 1239 1239 #1238 | | 2 9 3 |#18 7 5 | 18 6 4 | :-------------+--------------+------------------: | 5 7 8 | 6 13 4 | 123 123 9 | | 9 4 2 | 7 13 8 | 136 5 #136 | | 36 13 16 | 2 5 9 | 48 47 78 | :-------------+--------------+------------------: |#36 5 7 |#39 46 12 | 49 8 12 | | 8 123 #16 | 5 49 123 | 7 49 #1236 | | 4 123 9 | 18 68 7 | 1236 123 5 | '-------------'--------------'------------------' 3r1c9 - 3r1c4 =========================.. || \\ (3-8)r2c9 = 8r2c5 - (8=1)r3c4 - 1r2c6 = 3r2c6 -. || \ (3-6)r5c9 = 6r8c9 - 6r8c3 = (6-3)r7c1 = 3r7c4 | || \ | 3r8c9 -------------------------------------- 3r8c6

kraken column (3)r1258c9
-3r8c6 stte

even tho this ended up much longer than id normally be happy with, it was fun to map out! very curious to know your own path for it

Website · by **denis_berthier** » Tue Sep 21, 2021 6:41 am

.
SER = 8.3

I like this puzzle because it illustrates perfectly how additional requirements about the number of steps can transform an easy puzzle into a hard one.

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 1 8 4 ! 239 29 6 ! 5 2379 237 ! ! 7 6 5 ! 4 1289 123 ! 12389 1239 1238 ! ! 2 9 3 ! 18 7 5 ! 18 6 4 ! +----------------------+----------------------+----------------------+ ! 5 7 8 ! 6 123 4 ! 123 123 9 ! ! 9 4 126 ! 7 123 8 ! 1236 5 1236 ! ! 36 123 126 ! 12 5 9 ! 12468 1247 12678 ! +----------------------+----------------------+----------------------+ ! 36 5 7 ! 1239 12469 123 ! 123469 8 1236 ! ! 8 123 126 ! 5 12469 123 ! 7 12349 1236 ! ! 4 123 9 ! 1238 1268 7 ! 1236 123 5 ! +----------------------+----------------------+----------------------+ 148 candidates.

This puzzle has a solution in S+W5, or even in the simplest S+Z5 (Subsets + z-chains; i.e. only reversible patterns) - which is a priori not very hard. In these resolution theories, the simplest-first strategy finds 30 relatively elementary non-W1 steps.

Here is the S+Z5 solution: Show

[Edit: the solution I had first given was in Z5 only, without Subsets]

After checking there's no 1- or 2- step solution with whips of length ≤ 8, I tried the (very slow) SudoRules fewer step algorithm in S+W8
The first two tries gave solutions with 10 steps - a significant reduction in the number of steps, at the cost of using harder and longer chains than necessary.
The third try gave a solution with 9 steps. I stopped after 9 tries, which didn't give a shorter path. Here is the result of the 3rd try:

Code: Select all: =====> STEP #1 hidden-triplets-in-a-row: r6{n4 n7 n8}{c7 c8 c9} ==> r6c9≠1, r6c9≠6, r6c9≠2, r6c8≠2, r6c8≠1, r6c7≠6, r6c7≠2, r6c7≠1 whip[1]: r6n6{c3 .} ==> r5c3≠6 =====> STEP #2 hidden-pairs-in-a-block: b9{n4 n9}{r7c7 r8c8} ==> r7c7≠3, r8c8≠3, r8c8≠2, r8c8≠1, r7c7≠6, r7c7≠2, r7c7≠1 =====> STEP #3 hidden-pairs-in-a-row: r8{n4 n9}{c5 c8} ==> r8c5≠6, r8c5≠2, r8c5≠1 =====> STEP #4 biv-chain[5]: r7n4{c5 c7} - r6c7{n4 n8} - r3n8{c7 c4} - b8n8{r9c4 r9c5} - b8n6{r9c5 r7c5} ==> r7c5≠2, r7c5≠1, r7c5≠9 =====> STEP #5 whip[7]: r1c5{n2 n9} - c4n9{r1 r7} - r8c5{n9 n4} - c8n4{r8 r6} - c8n7{r6 r1} - r1n2{c8 c9} - r7n2{c9 .} ==> r2c6≠2 whip[1]: c6n2{r8 .} ==> r7c4≠2, r9c4≠2, r9c5≠2 =====> STEP #6 whip[8]: r3c4{n1 n8} - r9c4{n8 n3} - r7c4{n3 n9} - r8c5{n9 n4} - c8n4{r8 r6} - c8n7{r6 r1} - r1n3{c8 c9} - b9n3{r7c9 .} ==> r6c4≠1 naked-single ==> r6c4=2 hidden-single-in-a-block ==> r5c3=2 whip[1]: b5n1{r5c5 .} ==> r2c5≠1, r9c5≠1 =====> STEP #7 finned-x-wing-in-rows: n9{r8 r1}{c8 c5} ==> r2c5≠9 whip[1]: r2n9{c8 .} ==> r1c8≠9 =====> STEP #8 whip[7]: r1n3{c9 c4} - r1n9{c4 c5} - r8c5{n9 n4} - r7c5{n4 n6} - r9n6{c5 c7} - r9n3{c7 c2} - r7c1{n3 .} ==> r2c8≠3 =====> STEP #9 whip[6]: c9n8{r6 r2} - r2c5{n8 n2} - r1c5{n2 n9} - r8n9{c5 c8} - r2c8{n9 n1} - r3c7{n1 .} ==> r6c9≠7 stte

François, I think your algorithm is much faster than mine. Could you try this puzzle? I think it's possible to get less than 9 steps in W8.
[Edit] W8 instead of W7 - thanks François

Website · by **denis_berthier** » Tue Sep 21, 2021 6:56 am

Hi Shye
Trying to understand how you count steps. I added my count in blue. Can you correct me if I misinterpreted?

shye wrote:the path i got was 4 steps
STEP 1:
Code: Select all
1r45c7 - 1r3c7 ================ 1r3c4 // \\ 1r45c5 \\ => -1r6c4 \\ \\ 6r5c7 - 6r9c7 = (6-8)r9c5 = 8r2c5 - 8r3c4

STEP 2:
UR chain
23UR in r45c57, guardians 1r45c57 & 6r5c7

few singles and locked candidates

STEP 3:
(4=8)r6c7 - 8r6c9 = 8r2c9 - 8r2c5 = (8-6)r9c5 = (6-4)r7c5 = 4r7c7 - 4r6c7 loop
=> -8r2c7, -2r9c5, -29r7c5

STEP 4:
l-wing
1r3c4 = (1-3)r2c6 = (3-9)r1c4 = 9r7c4
=> -1r7c4

STEPS 5 to XXX:
some pairs, then the hard step:

STEP XXX+1:
Code: Select all
3r1c9 - 3r1c4 =========================.. || \\ (3-8)r2c9 = 8r2c5 - (8=1)r3c4 - 1r2c6 = 3r2c6 -. || \ (3-6)r5c9 = 6r8c9 - 6r8c3 = (6-3)r7c1 = 3r7c4 | || \ | 3r8c9 -------------------------------------- 3r8c6

kraken column (3)r1258c9
-3r8c6 stte

Could you say how many pairs there are in what I've numbered steps 5 to XXX?
Trying also to see which rating your last step would be granted in my approach (number of CSP-Variables used - basically the number of = signs, counting only one for the vertical 3 (CSP-Variable c9n3): 8
I'd call the pattern a super-forcing-braid[8] - the "super" because it starts from 4 possibilities instead of the 2 for forcing-braids.

Website · by **denis_berthier** » Tue Sep 21, 2021 8:09 am

.
As shye, I suppose there's some trick to simlipfy the solution. And as the puzzle was proposed by eleven, I guess it might be related to variable replacement. So, here are all the views for the resolution state after Singles and whips[1]:

Code: Select all: standard rc-view: Physical rows are rows, physical columns are columns. Data are digits. 1 8 4 239 29 6 5 2379 237 7 6 5 4 1289 123 12389 1239 1238 2 9 3 18 7 5 18 6 4 5 7 8 6 123 4 123 123 9 9 4 126 7 123 8 1236 5 1236 36 123 126 12 5 9 12468 1247 12678 36 5 7 1239 12469 123 123469 8 1236 8 123 126 5 12469 123 7 12349 1236 4 123 9 1238 1268 7 1236 123 5 The following representations, first introduced in the "Hidden Logic of Sudoku" (HLS, 2007), may be used e.g. to more easily spot: rn-, cn- or bn- bivalue pairs (also named bilocal pairs), mono-typed-chains (the 2D-chains of HLS), Hidden Subsets and Fishes (which will appear as Naked Subsets in the proper space). rn-view: Physical rows are rows, physical columns are digits. Data are columns. 1 4589 489 3 7 6 89 2 458 56789 56789 6789 4 3 2 1 579 578 47 1 3 9 6 8 5 47 2 578 578 578 6 1 4 2 3 9 3579 3579 579 2 8 379 4 6 1 234789 234789 12 78 5 1379 89 79 6 45679 45679 14679 57 2 1579 3 8 457 235689 235689 2689 58 4 359 7 1 58 24578 24578 2478 1 9 57 6 45 3 cn-view: Physical rows are columns, physical columns are digits. Data are rows. 1 3 67 9 4 67 2 8 5 689 689 689 5 7 2 4 1 3 568 568 3 1 2 568 7 4 9 3679 1679 179 2 8 4 5 39 17 245789 1245789 45 78 6 789 3 29 1278 278 278 278 4 3 1 9 5 6 2345679 245679 24579 67 1 5679 8 236 27 24689 124689 12489 68 5 3 16 7 128 25678 125678 12578 3 9 5678 16 26 4 bn-view: Physical rows are blocks, physical columns are digits. Data are positions in a block. 1 7 9 3 6 5 4 2 8 567 1256 16 4 9 3 8 57 125 4567 23456 23456 9 1 8 23 467 245 689 689 78 5 1 679 2 3 4 257 257 25 3 8 1 4 6 9 1246789 1246789 1246 78 5 4679 89 79 3 568 568 158 7 2 16 3 4 9 1235678 1235678 1367 25 4 258 9 78 125 135678 135678 135678 15 9 1367 4 2 15

It appears there are several opportunities for replacements, but I don't have time to explore this idea further.

by **totuan** » Tue Sep 21, 2021 8:43 am

Code: Select all: *--------------------------------------------------------------------* | 1 8 4 | 239 29 6 | 5 2379 237 | | 7 6 5 | 4 1289 123 | 1289-3 1239 1238 | | 2 9 3 | 18 7 5 | 18 6 4 | |----------------------+----------------------+----------------------| | 5 7 8 | 6 123 4 | 123 123 9 | | 9 4 12 | 7 123 8 | 1236 5 1236 | | 36 123 126 | 12 5 9 | 48 47 78 | |----------------------+----------------------+----------------------| | 36 5 7 | 1239 12469 123 | 49 8 1236 | | 8 123 126 | 5 49 123 | 7 49 1236 | | 4 123 9 | 128-3 1268 7 | 1236 123 5 | *--------------------------------------------------------------------*

This one is not hard to solve but quite hard to find one step. Many (123) on grid, my path’s 5 steps and not nice

. Maybe eleven has a nice one.
01: (3)r2c6=(3-9)r1c4=r7c4-r7c7=r2c7 => r2c7<>3
02: Present as diagram: => r9c4<>3

Code: Select all: (3)r2c8-(3)r2c6=r1c4* || (3-7)r1c8=(7-4)r6c8=r6c7-r7c7=(4-6)r7c5=(6-8)r9c5=r9c4* || (3)r4c8=r45c7=r9c7* || (3)r9c8*

Code: Select all: *--------------------------------------------------------------------* | 1 8 4 | 39 29 6 | 5 2379 27-3 | | 7 6 5 | 4 1289 123 | 1289 1239 128-3 | | 2 9 3 | 18 7 5 | 18 6 4 | |----------------------+----------------------+----------------------| | 5 7 8 | 6 123 4 | 123 123 9 | | 9 4 12 | 7 123 8 | 1236 5 1236 | | 36 123 126 | 12 5 9 | 48 47 78 | |----------------------+----------------------+----------------------| | 36 5 7 | 39 12469 123 | 49 8 1236 | | 8 123 126 | 5 49 123 | 7 49 1236 | | 4 123 9 | 128 1268 7 | 1236 123 5 | *--------------------------------------------------------------------*

03: (3)r2c6=(3)r1c4-(3=9)r7c4-(9=4)r7c7-(4=8)r6c7-r6c9=r2c9 => r2c9<>3
04: (3)r1c4=r7c4-(3=6)r7c1-r7c5=(68)r9c45-r3c4=r3c7-(8=4)r6c7-(4=7)r6c8-r1c8=r1c9 => r1c9<>3

Code: Select all: *--------------------------------------------------------------------* | 1 8 4 | 39 29 6 | 5 379 27 | | 7 6 5 | 4 1289 123 | 1289 39 128 | | 2 9 3 | 18 7 5 | 18 6 4 | |----------------------+----------------------+----------------------| | 5 7 8 | 6 123 4 | 123 12 9 | | 9 4 12 | 7 123 8 | 1236 5 1236 | | 36 123 126 | 12 5 9 | 48 47 78 | |----------------------+----------------------+----------------------| | 36 5 7 | 39 1249-6 123 | 49 8 1236 | | 8 123 126 | 5 49 123 | 7 49 1236 | | 4 123 9 | 128 1268 7 | 1236 12 5 | *--------------------------------------------------------------------*

05: (6)r9c5=(6-3)r9c7=r9c2-(3=6)r7c1 => r7c5<>6, stte
I can reduce to 3 steps by one more diagram.

For anyone likes one step

.

Code: Select all: *--------------------------------------------------------------------* | 1 8 4 |@239 29 6 | 5 #2379 237 | | 7 6 5 | 4 1289 @123 |#12389 @1239 #1238 | | 2 9 3 | 18 7 5 | 18 6 4 | |----------------------+----------------------+----------------------| | 5 7 8 | 6 123 4 | 123 #123 9 | | 9 4 12 | 7 123 8 | 1236 5 1236 | | 36 123 126 | 12 5 9 | 48 47 78 | |----------------------+----------------------+----------------------| | 36 5 7 |#1239 1249-6 123 | 49 8 1236 | | 8 123 126 | 5 49 123 | 7 49 1236 | | 4 #123 9 |@1238 1268 7 |#1236 @123 5 | *--------------------------------------------------------------------*

Look at 3’s: if removing 3’s on # cells => based one 3’s on @ cells then invalid 3’s B2.
Present as diagram: => r7c5<>6, stte

Code: Select all: DP 3’s || (3-9)r7c4=(49)r78c5* || (3-7)r1c8=(7-4)r6c8=(49)r67c7-r7c4=r1c4 || (3)r2c7-----(9)r3c7=(9-4)r7c7=r7c5* || | || (3)r2c7 || || (3)r4c8--(3)r45c7 || || || (3)r9c7 || | (3)r9c7----(6)r9c7=r9c5* || (3-8)r2c9=r6c9-(8=4)r6c7-r7c7=r7c5* || (3)r9c2-(3=6)r7c1*

Thanks for nice puzzle.
totuan

by **eleven** » Tue Sep 21, 2021 10:06 am

Thanks for your great efforts. I hoped there would be a more elegant solution. My shark has 5 fins.
As soon as one of the 3's in r1c49, r9c4 is eliminated, you have no chance to spot it anymore.

Code: Select all: *--------------------------------------------------------------------* | 1 8 4 | #239 29 6 | 5 *2379 a#237 | | 7 6 5 | 4 f1289 123 | 12389 1239 *123-8 | | 2 9 3 | 18 7 5 | 18 6 4 | |-------------------+-----------------------+------------------------| | 5 7 8 | 6 123 4 | 123 123 9 | | 9 4 12 | 7 123 8 | c1236 5 *1236 | | 36 123 126 | 12 5 9 | 48 47 b78 | |-------------------+-----------------------+------------------------| | g36 5 7 | *1239 h12469 123 | 49 8 #1236 | | 8 123 126 | 5 49 123 | 7 49 #1236 | | 4 *123 9 | #1238 e1268 7 |d#1236 #123 5 | *--------------------------------------------------------------------*

Oddagon 3 (r1c4,r178c9,r9c784) with 5 guardians:
3r2c9
(3-7)r1c8 = 78r16c9
(3-6)r5c9 = r5c7 - r9c7 = (6-8)r9c5 = 8r2c5
3r7c4 | r9c2 - (3=6)r7c1 - r7c5 = (6-8)r9c5 = 8r2c5
=> -8r2c9, stte

by **DEFISE** » Tue Sep 21, 2021 10:31 am

denis_berthier wrote:.
François, I think your algorithm is much faster than mine. Could you try this puzzle? I think it's possible to get less than 9 steps in W7.

Hi Denis,
your 9 steps solution is in W8, not in W7 !
With my initial algo: in W7 the best I found is 10 steps (with 30 tries).
But in W8 I found this 6 steps solution, with only 2 whips, on the 4th try:
N.B1: less than 12s by try.
N.B2: My initial algo seeks to minimize the number of whips. Then I count the subsets by hand.

14 singles
Bloc/line : 3b4r6 => -3r6c4 -3r6c7 -3r6c8 -3r6c9
Bloc/line : 3b5c5 => -3r1c5 -3r2c5 -3r7c5 -3r8c5 -3r9c5
Hidden pairs: 49r8c58 => -1r8c5 -2r8c5 -6r8c5 -1r8c8 -2r8c8 -3r8c8
Hidden pairs: 49b9p15 => -1r7c7 -2r7c7 -3r7c7 -6r7c7
Hidden triplets: 478r6c789 => -1r6c7 -2r6c7 -6r6c7 -1r6c8 -2r6c8 -1r6c9 -2r6c9 -6r6c9
Bloc/line : 6r6b4 => -6r5c3
whip[7]: r9n8{c4 c5}- c5n6{r9 r7}- r7n4{c5 c7}- r6n4{c7 c8}- c8n7{r6 r1}- r1n3{c8 c9}- b9n3{r7c9 .} => -3r9c4
Hidden pairs: 39c4r17 => -2r1c4 -1r7c4 -2r7c4
whip[8]: c5n8{r2 r9}- r9n6{c5 c7}- r5n6{c7 c9}- r8n6{c9 c3}- r7c1{n6 n3}- r9n3{c2 c8}- c9n3{r7 r1}- c4n3{r1 .} => -8r2c9
STTE

by **totuan** » Tue Sep 21, 2021 11:01 am

eleven wrote:My shark has 5 fins.

Nice find! First time I solve puzzle based on this concept, so my shark has 7 fins :lol:

Again, thanks for your puzzle.
totuan

Website · by **denis_berthier** » Tue Sep 21, 2021 11:09 am

DEFISE wrote:
denis_berthier wrote:.
François, I think your algorithm is much faster than mine. Could you try this puzzle? I think it's possible to get less than 9 steps in W7.

your 9 steps solution is in W8, not in W7 !

OK, corrected

DEFISE wrote:With my initial algo: in W7 the best I found is 10 steps (with 30 tries).
But in W8 I found this 6 steps solution, with only 2 whips, on the 4th try

Great!
So, now you can also have Subsets in the algo!

Website · by **denis_berthier** » Tue Sep 21, 2021 11:22 am

eleven wrote:Thanks for your great efforts. I hoped there would be a more elegant solution. My shark has 5 fins.
As soon as one of the 3's in r1c49, r9c4 is eliminated, you have no chance to spot it anymore.
Code: Select all
*--------------------------------------------------------------------* | 1 8 4 | #239 29 6 | 5 *2379 a#237 | | 7 6 5 | 4 f1289 123 | 12389 1239 *123-8 | | 2 9 3 | 18 7 5 | 18 6 4 | |-------------------+-----------------------+------------------------| | 5 7 8 | 6 123 4 | 123 123 9 | | 9 4 12 | 7 123 8 | c1236 5 *1236 | | 36 123 126 | 12 5 9 | 48 47 b78 | |-------------------+-----------------------+------------------------| | g36 5 7 | *1239 h12469 123 | 49 8 #1236 | | 8 123 126 | 5 49 123 | 7 49 #1236 | | 4 *123 9 | #1238 e1268 7 |d#1236 #123 5 | *--------------------------------------------------------------------*

Oddagon 3 (r1c4,r178c9,r9c784) with 5 guardians:
3r2c9
(3-7)r1c8 = 78r16c9
(3-6)r5c9 = r5c7 - r9c7 = (6-8)r9c5 = 8r2c5
3r7c4 | r9c2 - (3=6)r7c1 - r7c5 = (6-8)r9c5 = 8r2c5
=> -8r2c9, stte

Starting from the same PM (obtained after more eliminations than mere Subsets and whips[1]):

Code: Select all: +-------------------+-------------------+-------------------+ ! 1 8 4 ! 239 29 6 ! 5 2379 237 ! ! 7 6 5 ! 4 1289 123 ! 12389 1239 1238 ! ! 2 9 3 ! 18 7 5 ! 18 6 4 ! +-------------------+-------------------+-------------------+ ! 5 7 8 ! 6 123 4 ! 123 123 9 ! ! 9 4 12 ! 7 123 8 ! 1236 5 1236 ! ! 36 123 126 ! 12 5 9 ! 48 47 78 ! +-------------------+-------------------+-------------------+ ! 36 5 7 ! 1239 12469 123 ! 49 8 1236 ! ! 8 123 126 ! 5 49 123 ! 7 49 1236 ! ! 4 123 9 ! 1238 1268 7 ! 1236 123 5 ! +-------------------+-------------------+-------------------+

I can't find any oddagon. To which definition of an oddagon are you referring?

by **DEFISE** » Tue Sep 21, 2021 11:42 am

denis_berthier wrote:So, now you can also have Subsets in the algo!

No, my initial algo tries only to minimize the number of whips and then I count subsets by hand.
You certainly read my previous post before I added the N.B.2 to it.
My second algo tries all possible combinations of rules (subsets + whips) but is of course much slower. I haven't used it here. It can be interesting when there are a lot of subsets, like in mith's puzzles.

Website · by **denis_berthier** » Tue Sep 21, 2021 12:16 pm

.
As none of the proposed solutions was very subtle, I wondered why not try the nukes?

Starting from the RS after Singles and Whips[1], a 1-step solution:

FORCING[3]-T&E(W1) applied to trivalue candidates n2r1c9, n3r1c9 and n7r1c9 :
===> 3 values decided in the three cases: n6r7c1 n3r6c1 n6r6c3
===> 63 candidates eliminated in the three cases: n2r1c4 n2r1c8 n9r1c8 n2r2c5 n9r2c5 n2r2c6 n1r2c7 n3r2c7 n8r2c7 n1r2c8 n2r2c9 n3r2c9 n2r4c5 n2r4c7 n3r4c8 n6r5c3 n2r5c5 n1r5c7 n3r5c7 n1r5c9 n2r5c9 n6r6c1 n3r6c2 n1r6c3 n2r6c3 n1r6c7 n2r6c7 n6r6c7 n1r6c8 n2r6c8 n1r6c9 n2r6c9 n6r6c9 n3r7c1 n1r7c4 n2r7c4 n1r7c5 n6r7c5 n2r7c6 n3r7c6 n1r7c7 n2r7c7 n3r7c7 n6r7c7 n1r7c9 n6r7c9 n1r8c2 n2r8c2 n6r8c3 n1r8c5 n2r8c5 n4r8c5 n1r8c6 n1r8c8 n2r8c8 n3r8c8 n2r8c9 n3r8c9 n3r9c4 n1r9c5 n2r9c5 n1r9c7 n2r9c7

Code: Select all: +-------------+-------------+-------------+ ! 1 8 4 ! 39 29 6 ! 5 37 237 ! ! 7 6 5 ! 4 18 13 ! 29 239 18 ! ! 2 9 3 ! 18 7 5 ! 18 6 4 ! +-------------+-------------+-------------+ ! 5 7 8 ! 6 13 4 ! 13 12 9 ! ! 9 4 12 ! 7 13 8 ! 26 5 36 ! ! 3 12 6 ! 12 5 9 ! 48 47 78 ! +-------------+-------------+-------------+ ! 6 5 7 ! 39 249 1 ! 49 8 23 ! ! 8 3 12 ! 5 69 23 ! 7 49 16 ! ! 4 123 9 ! 128 68 7 ! 36 123 5 ! +-------------+-------------+-------------+

stte

by **marek stefanik** » Tue Sep 21, 2021 7:34 pm

eleven wrote:
Code: Select all
*--------------------------------------------------------------------* | 1 8 4 | #239 29 6 | 5 *2379 a#237 | | 7 6 5 | 4 f1289 123 | 12389 1239 *123-8 | | 2 9 3 | 18 7 5 | 18 6 4 | |-------------------+-----------------------+------------------------| | 5 7 8 | 6 123 4 | 123 123 9 | | 9 4 12 | 7 123 8 | c1236 5 *1236 | | 36 123 126 | 12 5 9 | 48 47 b78 | |-------------------+-----------------------+------------------------| | g36 5 7 | *1239 h12469 123 | 49 8 #1236 | | 8 123 126 | 5 49 123 | 7 49 #1236 | | 4 *123 9 | #1238 e1268 7 |d#1236 #123 5 | *--------------------------------------------------------------------*

Oddagon 3 (r1c4,r178c9,r9c784) with 5 guardians:
3r2c9
(3-7)r1c8 = 78r16c9
(3-6)r5c9 = r5c7 - r9c7 = (6-8)r9c5 = 8r2c5
3r7c4 | r9c2 - (3=6)r7c1 - r7c5 = (6-8)r9c5 = 8r2c5
=> -8r2c9, stte

Nice move!
Can't believe I missed that when looking at the impossible 3-rookery (instead of that I got a more complicated version which was completely useless in the puzzle).

It's amazing how complicated it can be to decide if a 3-rookery has solutions.
I wonder what would a computer's path look like if it weren't given any 123s at all (considering the puzzle solved after all other digits have been correctly placed).

I've had a look at possible replacements, it seems that 1r9c8, 2r4c8 reduces the rating the most (it can then be solved with AICs without ALSs), but I don't think it helps with the number of steps.

Marek

by **shye** » Tue Sep 21, 2021 11:50 pm

eleven wrote:Thanks for your great efforts. I hoped there would be a more elegant solution. My shark has 5 fins.
As soon as one of the 3's in r1c49, r9c4 is eliminated, you have no chance to spot it anymore.

Oddagon 3 (r1c4,r178c9,r9c784) with 5 guardians

wow! very fancy deduction, more guardians than i'd normally check for :lol:

denis_berthier wrote:Hi Shye
Trying to understand how you count steps. I added my count in blue. Can you correct me if I misinterpreted?
...
Could you say how many pairs there are in what I've numbered steps 5 to XXX?

the UR chain in the first diagram is all one step, i just added some wording for it below. unless youre counting the locked 1s instead which is important for the l-wing later on, which case thats fine
there are two pairs that occur after the l-wing, but only the hidden 12 pair in r7 is needed, so to minimise steps only count that one

i usually consider locked candidates and hidden/naked tuples as not-a-step, but if we do count them in then my path would be a total of 6. but i guess at this point why not break down the last step into something more palatable (im not a fan of how the chain implies a 3 in r2c9 and r2c6 simultaneously, that much would be better split into two)

Code: Select all: .-------------.---------------.------------------. | 1 8 4 | 39 29 6 | 5 2379 237 | | 7 6 5 | 4 #289 #13 | 1239 1239 #128-3| | 2 9 3 |#18 7 5 | 18 6 4 | :-------------+---------------+------------------: | 5 7 8 | 6 13 4 | 123 123 9 | | 9 4 2 | 7 13 8 | 136 5 136 | | 36 13 16 | 2 5 9 | 48 47 78 | :-------------+---------------+------------------: | 36 5 7 | 39 46 12 | 49 8 12 | | 8 123 16 | 5 49 123 | 7 49 1236 | | 4 123 9 | 138 68 7 | 1236 123 5 | '-------------'---------------'------------------'

(3=1)r2c6 - (1=8)r3c4 - 8r2c5 = 8r2c9
=> -3r2c9

Code: Select all: .-------------.---------------.------------------. | 1 8 4 |#39 29 6 | 5 2379 #237 | | 7 6 5 | 4 289 #13 | 1239 1239 128 | | 2 9 3 | 18 7 5 | 18 6 4 | :-------------+---------------+------------------: | 5 7 8 | 6 13 4 | 123 123 9 | | 9 4 2 | 7 13 8 | 136 5 #136 | | 36 13 16 | 2 5 9 | 48 47 78 | :-------------+---------------+------------------: |#36 5 7 |#39 46 12 | 49 8 12 | | 8 123 #16 | 5 49 12-3| 7 49 #1236 | | 4 123 9 | 138 68 7 | 1236 123 5 | '-------------'---------------'------------------' 3r1c9 - 3r1c4 ========================== 3r2c6 || \ (3-6)r5c9 = 6r8c9 - 6r8c3 = (6-3)r7c1 = 3r7c4 \ || \ \ 3r8c9 ------------------------------------- 3r8c6

kraken column (3)r158c9
-3r8c6 stte

The New Sudoku Players' Forum

Gata de mar

Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar

Re: Gata de mar